通过RPA对一维碳链的新见解
New insights into the 1D carbon chain through the RPA
摘要：
采用密度泛函理论和无规相近似方法研究了无限长线性碳链（碳炔）的电子和结构性质.研究是在真空中进行的，并为碳纳米管（CNT）内的碳炔。在真空中，半局域DFT和RPA预测键长交替分别约为0.04 π和0.13 π。对于DFT和RPA，在$Γ$点处的最高光学模式的频率为1219 cm $^{-1}$，并且约为2000 cm $^{-1}$。RPA的协议，以前的高层次量子化学和扩散蒙特卡罗结果是极好的。对于RPA，我们计算的声子色散在整个布里渊区，并找到显着的定量差异DFT计算不仅在$Γ$点，但也在整个布里渊区。为了模拟碳纳米管内的碳炔，我们考虑了（10，0）CNT。在这里，DFT计算甚至对k点采样定性敏感。在一个非常密集的k点采样的limes，半局部DFT预测没有键长交替（BLA），而在RPA中，一个相当大的BLA为0.09 μ m。减少的BLA导致约350 cm $^{-1}$的振动频率的显著红移，因此它们与实验估计很好地一致。总的来说，RPA和以前报道的相关波函数方法和实验拉曼数据的结果之间的良好协议表明，RPA提供了可靠的结果在适度的计算成本。因此，它提出了一个有用的除了相关的波函数方法的剧目和它的准确性显然占主导地位的低维系统，半局部密度泛函的斗争，甚至产生定性正确的结果。
英文摘要：
We investigated the electronic and structural properties of the infinite linear carbon chain (carbyne) using density functional theory (DFT) and the random phase approximation (RPA) to the correlation energy. The studies are performed in vacuo and for carbyne inside a carbon nano tube (CNT). In the vacuum, semi-local DFT and RPA predict bond length alternations of about 0.04 Å and 0.13 Å, respectively. The frequency of the highest optical mode at the $Γ$ point is 1219 cm$^{-1}$ and about 2000 cm$^{-1}$ for DFT and the RPA. Agreement of the RPA to previous high level quantum chemistry and diffusion Monte-Carlo results is excellent. For the RPA we calculate the phonon-dispersion in the full Brillouine zone and find marked quantitative differences to DFT calculations not only at the $Γ$ point but also throughout the entire Brillouine zone. To model carbyne inside a carbon nanotube, we considered a (10,0) CNT. Here the DFT calculations are even qualitatively sensitive to the k-points sampling. At the limes of a very dense k-points sampling, semi-local DFT predicts no bond length alternation (BLA), whereas in the RPA a sizeable BLA of 0.09 Å prevails. The reduced BLA leads to a significant red shift of the vibrational frequencies of about 350 cm$^{-1}$, so that they are in good agreement with experimental estimates. Overall, the good agreement between the RPA and previously reported results from correlated wavefunction methods and experimental Raman data suggests that the RPA provides reliable results at moderate computational costs. It hence presents a useful addition to the repertoire of correlated wavefunction methods and its accuracy clearly prevails for low dimensional systems, where semi-local density functionals struggle to yield even qualitatively correct results.
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